Timeline for Markov chains: invariant measures and explosion
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 28, 2012 at 12:14 | comment | added | Yuri Bakhtin | @Nathanael Berestycki: A measure is invariant if it is preserved by the Markov semigroup (i.e., if you start the process with this initial distribution, then for any positive time the distribution stays the same). This measure is not preserved since the mass is driven to infinity and for any finite subset A of S, the probability that the process is in A goes to zero as time goes to infinity. | |
| Aug 25, 2012 at 7:49 | comment | added | Nathanael Berestycki | It is a classical (and surprising) feature of continuous Markov chains that they can have an invariant measure while being transient. See, for instance, section 3.5 in James Norris' book on Markov chains. (Notice that the definition of invariant measure is the usual one and does not require the process to be recurrent or non-explosive). In any case, no matter how you would call such a measure, I hope you'll agree it is interesting to know what it means for the process... | |
| Aug 23, 2012 at 18:44 | history | answered | Yuri Bakhtin | CC BY-SA 3.0 |